How to define uniformly ticking clock defined in GR?

1. Sep 29, 2013

center o bass

I just read the following definition of a clock in GR:

"A clock is a smooth embedding γ : t → γ(t) from a real interval into M such that the tangent vector \dot{γ} (t) is everywhere timelike with respect to g and future-pointing. This terminology is justified because we can interpret the value of the parameter t as the reading of a clock. Note that our definition of a clock does not demand that “its ticking be uniform” in any sense. Only smoothness and monotonicity are required."

And I wondered how would a clock that is "ticking uniformly" be defined?

2. Sep 29, 2013

UltrafastPED

Since the spacetime intervals are relativistic invariants, and on a time-like path they are non-zero - you could start by trying uniform spacetime intervals and see how they do.

At least everybody would agree with the ticks ...

3. Sep 29, 2013

DrGreg

Using that notation, "ticking uniformly" would mean the length of the tangent vector $\dot{γ} (t)$ was constant.

The length of the tangent vector $\dot{γ} (t)$ is proportional to the ratio of proper time to clock time $\|\dot{γ} (t)\| = c\,d\tau/dt$.

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